There are two questions. Thank you inadvanced A medical researcher wishes to try three different techniques to lower blood pressure of patients with high blood pressure. Thesubjects are randomly selected and assigned to one of three groups. Group 1 is given medication, Group 2 is given anexercise program, and Group 3 is assigned a diet program. At the end of six weeks, the reduction in each subject's bloodGroup 1GroupGroup 31297pressure is recorded. Use the Kruskal-Wallis test to find the critical value to test the claim that there is no difference in thedistribution of the populations. Use a = 0.05.1361310316491451015O A. 4.153О В. 5.991О с. 3.195O D. 1.960 A researcher wants to know if the time spent in prison for a particular type of crime was the same for men and women.A random sample of men and women were each asked to give the length of sentence received. The data, in years, arelisted to the right. Use the Wilcoxon rank sum test to find R, the sum of the ranks for the smaller sample, to test theMen13 25 1921 22 29Women121512172915claim that there is no difference in the sentence received by each gender.Men17 251522 26 27Women37 1113162030(.....O A. 115.5O B. 155.5O C. 173.5OD125.5

The Wilcoxon rank sum test is a non parametric test and it used to compares the two independent group medians when the data contains outlier in the data set. The Wilcoxon rank sum test is denoted with R and it is given by R = min ( sum of ranks of group1 , sum of ranks of group2) Given level of significance α = 0.05 No of Groups are K = 3 then degrees of freedom is df = K -1 = 3 -1 =2 Thus, from the Kruskal -Wallis H table values, the critical value with df = 2 at 0.05 level of significance is 5.991 Therefore, the critical value of the test is 5.991 Option (b) is correct Arrange the two groups data in ascending order and then find the ranks for data by combining as shown below, (remember the data point group) Men Women Ranks of men Ranks of women 13 11 4.5 1 15 12 7 2.5 17 12 10.5 2.5 19 13 12 4.5 21 15 14 7 22 15 15.5 7 22 16 15.5 9 25 17 17.5 10.5 25 20 17.5 13 26 29 19 21.5 27 30 20 23 29 37 21.5 24 sum of ranks for men = 174.5 sum of ranks for Women =125.5 From the above table, we have sum of ranks for men = 174.5 sum of ranks for Women =125.5 R = min ( sum of ranks of group1 , sum of ranks of group2) = min(174.5 , 125.5) = 125.5 Hence, the R value is 125.5 i.e., Option (D) is correct